Question

how is the rate of change of a linear function related to the slope of its graph?

select all that apply

a. the greater the rate of change, the steeper the graph.
b. the smaller the rate of change, the shallower the graph.
c. the smaller the rate of change, the steeper the graph.
d. the greater the rate of change, the shallower the graph.

Explanation:

Define rate of change and slope

Using the Rate of Change Analysis knowledge point

• The rate of change of a linear function is equal to the slope of its graph.
• The magnitude (absolute value) of the slope determines the steepness of the line.

Analyze the relationship with steepness

Using the Rate of Change Analysis knowledge point

• A larger rate of change (larger slope magnitude) means the line rises or falls more quickly, resulting in a steeper graph.
• A smaller rate of change (smaller slope magnitude closer to zero) means the line rises or falls more slowly, resulting in a shallower (flatter) graph.

Evaluate the given options

Using the Rate of Change Analysis knowledge point

• Option A: "The greater the rate of change, the steeper the graph." This is correct.
• Option B: "The smaller the rate of change, the shallower the graph." This is correct.
• Option C: "The smaller the rate of change, the steeper the graph." This is incorrect.
• Option D: "The greater the rate of change, the shallower the graph." This is incorrect.

Answer:

• A. The greater the rate of change, the steeper the graph. (Correct answer)
• B. The smaller the rate of change, the shallower the graph. (Correct answer)
• C. The smaller the rate of change, the steeper the graph.
• D. The greater the rate of change, the shallower the graph.